Fractional Brownian motion and the critical dynamics of zipping polymers

Abstract

We consider two complementary polymer strands of length $L$ attached by a common end monomer. The two strands bind through complementary monomers and at low temperatures form a double stranded conformation (zipping), while at high temperature they dissociate (unzipping). This is a simple model of DNA (or RNA) hairpin formation. Here we investigate the dynamics of the strands at the equilibrium critical temperature $T=T_c$ using Monte Carlo Rouse dynamics. We find that the dynamics is anomalous, with a characteristic time scaling as $\tau \sim L^{2.26(2)}$, exceeding the Rouse time $\sim L^{2.18}$. We investigate the probability distribution function, the velocity autocorrelation function, the survival probability and boundary behaviour of the underlying stochastic process. These quantities scale as expected from a fractional Brownian motion with a Hurst exponent $H=0.44(1)$. We discuss similarities and differences with unbiased polymer translocation.

7 pages, 8 figures

References in corpus (11)

• In vivo anomalous diffusion and weak ergodicity breaking of lipid granules
• Anomalous Dynamics of Unbiased Polymer Translocation through a Narrow Pore
• Pore-blockade Times for Field-Driven Polymer Translocation
• Anomalous Polymer Dynamics Is Non-Markovian: Memory Effects and The Generalized Langevin Equation Formulation
• Asymptotic behavior of self-affine processes in semi-infinite domains
• Fractional Brownian motion approach to polymer translocation: the governing equation of motion
• Probability distributions for polymer translocation
• Comment on "Mean First Passage Time for Anomalous Diffusion"
• Probabilistic Phase Space Trajectory Description for Anomalous Polymer Dynamics
• Anomalous zipping dynamics and forced polymer translocation
• A lattice polymer study of DNA renaturation dynamics

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